SANTA CLARA — Discussions about Mike Nolan’s future as 49ers coach went into overtime Monday as the team postponed — then canceled — a news conference at team headquarters.

Nolan remained in meetings for hours with owner John York and team executive Jed York. The lengthy face-to-face discussions took place a day after the 49ers finished their season at 5-11.

The season-ending loss to the Cleveland Browns dropped Nolan’s coaching record to 16-32 over three seasons. That record, as well as Nolan’s awkward public feud with quarterback Alex Smith, leaves the coach’s employment status in jeopardy.

Apparently, the question of whether to fire Nolan or keep him was too difficult to solve in one day. The 49ers scheduled a news conference at 2 p.m., pushed it back to 4 p.m. — then abruptly pulled the plug on any public comments.

A team spokesman said late Monday afternoon only that there would be “no comments today” from York or Nolan. No timetable was set for an announcement.

According to the Associated Press, York and his son, Jed, drove away from the 49ers training complex at the same time as Nolan and his wife, Kathy.

“We met for some time today, and we’re going to meet again tomorrow,” the AP quoted John York as saying from the wheel of his car. “There’s no point in talking about this until we finish.”

“I’ve only got one thing to say — happy new year, and I’ll be back in the morning.” Nolan told AP.

Even the players were left in the dark. As they packed up their belongings and headed home for the offseason, several said they had no idea whether they would be working for the same boss in 2008.

“If I had say-so, all of them would come back,” rookie linebacker Patrick Willis said of the coaching staff. “But unfortunately, when things don’t go well, there’s always going to be a change. Something is going to change. You don’t know what.”

Right guard Justin Smiley, who missed the final eight games because of injury, said: “I have to say I’m a Nolan guy. Honestly. I like Coach Nolan. I hope that I can be back here. I think Dr. York is going to get it right, and I’d love to be a part of it.”

The status of Nolan’s staff also is in limbo. There was no word about much-maligned offensive coordinator Jim Hostler, whose unit finished last in the league in yards and points. The 49ers’ 219 points tied the franchise worst set in 1978.

A report that the 49ers would be interested in pursuing Detroit Lions offensive coordinator Mike Martz to run their offense was shot down by the team’s vice president of player personnel, Scot McCloughan.

“There’s no truth to that,” McCloughan said Sunday in reference to a Los Angeles Times report.

McCloughan, meanwhile, is expected to be promoted to general manager later this week. Such a move signals that, in the least, Nolan would be stripped of full control over personnel decisions, as had been promised him in his original contract.

Previously, McCloughan reported to Nolan, who had final say on roster matters.

With Nolan’s status on hold, the only coach fired Monday was Brian Billick of the Baltimore Ravens. Mike Singletary’s name immediately surfaces as a possible replacement.

Singletary, 49, was the Ravens inside linebackers coach for two seasons before joining Nolan’s staff as the assistant head coach/defense.

Singletary’s name is a hot one in the rumor mill across the country — he has also been linked to the Atlanta Falcons job — but the 49ers say no team has officially requested permission for a formal interview.

“I know that if he leaves, I’ll continue to work, continue to keep his lessons in my technique and play well,” said Willis, for whom Singletary served as a mentor. “So I’m thankful for what he’s taught me this year.”

While Singletary’s star is on the rise, Nolan spent Monday making his appeal for a second chance.

But of the 49ers’ five victories this season, only one came against a winning team: They beat Tampa Bay on Dec. 23, when the Buccaneers played their starters only sparingly in preparation for the playoffs.

Daniel Brown is a sports writer for the Bay Area News Group known for his award-winning profiles on subjects ranging from Jerry Rice to Sergio Romo to Taylor Swift. The Cotati native is a graduate of UC Davis.

Otto Warmbier was arrested in January 2016 at the end of a brief tourist visit to North Korea. He had been medically evacuated and was being treated at the University of Cincinnati Medical Center when he died at age 22.